Design and Realization of a Desktop Micro-Manipulation Cobotic Platform

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Design and Realization of a Desktop

Micro-Manipulation Cobotic Platform

Tianming Lu

To cite this version:

Tianming Lu. Design and Realization of a Desktop Micro-Manipulation Cobotic Platform. Automatic. Université Pierre et Marie Curie - Paris VI, 2016. English. �NNT : 2016PA066009�. �tel-01363790�

INSTITUT DES SYSTEMES INTELLIGENTS

ET DE ROBOTIQUE

UNIVERSITE PIERRE ET MARIE CURIE

PERCIPIO ROBOTICS

P H D T H E S I S

Tianming LU

Design and Realization of a

Desktop Micro-manipulation

Cobotic Platform

Thesis Advisors: Stéphane Régnier, David Heriban

defended on March 10, 2016

Jury :

Stéphane Viollet - CNRS Research Director Reviewer Philippe Fraisse - Professor at LIRMM / Université

Montpellier 2 Reviewer

Michaël Gauthier - CNRS Research Director Examinator David Heriban - CEO of Percipio Robotics Co-advisor Vincent Hayward - Professor at Université Pierre et

Marie Curie Examinator

Stéphane Régnier - Professor at Université Pierre et

Design and Realization of a Desktop Micro-manipulation Cobotic Platform

Abstract: Microrobotics is a fast growing eld of research and microsystems are in high demand from across a wide spectrum of our life. Nowadays, mass automation solutions are already available for large batch production of microsystems, while small batch production mainly relies on handmade processes due to the lack of ex-ible micro-manipulation system. Handmade processes have limited productivity and accuracy, which make it more and more dicult for small and medium-sized enter-prises to conquer their place on the international market. Under such circumstances, pioneer microrobotics company Percipio Robotics has proposed a desktop cobotic platform, Chronogrip, which aims to handle exible micro-manipulation. However, the solution is not yet complete and there are three main challenges to resolve:

• the dynamics of the piezoelectric stick-slip actuator is not fully understood, which delays the development of trajectory tracking strategies;

• existing haptic interfaces have limited bandwidth due to their mechanical prop-erties, consequently there is no available option that is able to render high dynamic haptic information from the microworld;

• for tweezers-based micro-manipulation in watchmaking process, no existing haptic interface is able to provide intuitive and eective operation.

The objective of thesis is to address these three issues. The rst part of the thesis is dedicated to the development of nonlinear dynamic model of the piezoelectric stick-slip actuator. The result shows that it is the rst dynamic model which can describe the actuator dynamics in time and frequency domain, for stepping and scanning mode, and for both forward and backward motion. The second part of the thesis is devoted to develop a method to extend the bandwidth of dual-stage haptic interface by using the signal crossover technique. The result shows that the bandwidth is uniformly extended to 1 kHz, which makes it possible to reproduce high dynamic phenomena from the microworld. The third part of the thesis aims to design an intuitive haptic interface for tweezers-based watchmaking operations. The design is also compatible with conventional tweezers-based usage. It is expected to integrate all of the three research results into the cobotic platform Chronogrip to enhance the productivity and eectiveness of micro-manipulation.

Keywords: Microrobotics; Micro-manipulation; Cobotics; Haptics; Nonlinear Dynamics; Piezoelectric Stick-Slip Actuator; Bandwidth; Signal Crossover; Haptic Tweezers.

iii Conception et Réalisation d'une Plate-forme de

Micro-manipulation Cobotique

Résumé: La microrobotique est un domaine de recherche en croissance rapide et les microsystèmes sont très demandés par un large éventail de notre vie. Aujourd'hui, des solutions d'automatisation massive sont déjà disponibles pour la production en série des microsystèmes, tandis que la production de petites quantités s'appuie prin-cipalement sur des processus manuels en l'absence de système de micro-manipulation exible. Un processus manuel impose des contraintes à la productivité et la préci-sion, ce qui accroît les dicultés pour les petites et moyennes entreprises à conquérir leur place sur le marché international. Dans ce contexte, la société pionnière pour la microrobotique Percipio Robotics a proposé une plate-forme cobotique, Chrono-grip, qui vise à gérer la micro-manipulation exible. Toutefois, la solution n'est pas encore complète et il y a trois principaux dés à résoudre:

• la dynamique de l'actionneur piézo-électrique stick-slip n'est pas entièrement comprise, ce qui retarde le développement des stratégies de suivi de trajectoire; • les interfaces haptiques ont peu de bande passante en raison des propriétés mécaniques, par conséquent il n'y a aucune option disponible qui soit capa-ble de reproduire des informations haptiques de haute dynamique depuis le micromonde;

• pour la micro-manipulation à la pince dans l'horlogerie, aucune interface hap-tique existante n'est en mesure d'assurer un fonctionnement intuitif et ecace. L'objectif de la thèse consiste à répondre à ces trois dés. La première partie de la thèse est consacrée à l'élaboration d'un modèle dynamique non-linéaire de l'actionneur piézo-électrique stick-slip. Le résultat montre qu'il est le premier mod-èle dynamique qui puisse décrire la dynamique de l'actionneur dans des domaines temporels et fréquentiels, pour les fonctionnements en sous-pas et en grand déplace-ment, et à la fois pour les directions vers l'avant et l'arrière. La deuxième partie de la thèse est consacrée à développer une méthode pour étendre la bande passante d'une interface haptique en double étage en utilisant la technique de signal crossover. Le résultat montre que la bande passante est uniformément étendue à 1 kHz, ce qui rend possible la reproduction des phénomènes de haute dynamique depuis le mi-cromonde. La troisième partie de la thèse vise à concevoir une interface haptique intuitive dédiée aux opérations d'horlogerie à la pince. Le design est également compatible avec l'utilisation conventionnelle d'une pince. Il est prévu d'intégrer tous les résultats de ces trois sujets de recherches dans la plate-forme de cobotique Chronogrip an d'améliorer la productivité et l'ecacité de la micro-manipulation. Mots-clés: Microrobotique; Micro-manipulation; Cobotique; Haptique; Dy-namique Non-linéaire; Actionneur Piézo-électrique Stick-Slip; Bande Passante; Sig-nal Crossover; Pince Haptique.

Contents

General Introduction 1 1 State-of-the-Art 5 1.1 Microrobotics . . . 6 1.1.1 Microworld . . . 6 1.1.2 Observation . . . 8 1.1.3 Micro-Manipulation Systems . . . 13 1.1.4 Chronogrip System . . . 15

1.1.5 Flexible Micro-Manipulation Solutions . . . 17

1.2 Actuators for Microrobotic Applications . . . 17

1.2.1 Piezoelectric Actuators . . . 18

1.2.2 Electrostatic Actuators. . . 20

1.2.3 Thermal Actuators . . . 21

1.2.4 Magneto-/Electrorheological Fluids . . . 22

1.2.5 Actuators for Microrobotic Applications . . . 22

1.2.6 Control Algorithm for Piezoelectric Stick-Slip Actuator. . . . 23

1.3 Haptic Interface . . . 24

1.3.1 Series-Structure Interface . . . 25

1.3.2 Parallel-Structure Interface . . . 27

1.3.3 Haptic Interfaces Summary . . . 29

1.3.4 Dedicated Haptic Interfaces for Micro-Manipulation . . . 29

1.4 Challenges . . . 29

2 Nonlinear modeling for a class of microrobotic systems using piezo-electric stick-slip actuators 33 2.1 Introduction . . . 35

2.2 State-of-the-Art . . . 36

2.2.1 Microrobotic Actuators . . . 36

2.2.2 Working Principle of Piezoelectric Stick-Slip Actuator . . . . 37

2.2.3 Friction Modeling. . . 38

2.3 Presentation of the microrobotic system . . . 40

2.4 Nonlinear dynamic modeling. . . 40

2.4.1 Dynamic Modeling of the PE and the slider . . . 41

2.4.2 Modeling of the Slider . . . 42

2.4.3 Modeling of the Friction . . . 43

2.5 Experimental analysis and identication . . . 48

2.5.1 Description of the experimental setup . . . 48

2.5.2 Parameters identication . . . 49

2.5.3 Model Validation . . . 53

vi Contents

2.7 Velocity Control . . . 57

2.8 Conclusions . . . 59

3 Extending the Bandwidth of Dual Stage Haptic Interface by Signal Crossover 61 3.1 Introduction . . . 63

3.2 State of the art . . . 65

3.3 System description . . . 66

3.3.1 Material description . . . 68

3.3.2 Crossover method . . . 69

3.4 Model and control . . . 72

3.4.1 Dynamic modeling . . . 72

3.4.2 Identication . . . 75

3.4.3 Compensation. . . 77

3.5 Experimental evaluation . . . 79

3.5.1 Performances of the haptic crossover method . . . 79

3.5.2 Optical tweezers application . . . 80

3.6 Conclusion. . . 82

4 Design of a Haptic Interface for Watchmakers 85 4.1 Introduction . . . 86

4.2 State-of-the-Art . . . 86

4.3 Technical Specications of the TéléTweez . . . 91

4.3.1 Description of Tweezers in Watchmaking Industries . . . 91

4.3.2 Description of Haptic Tweezers . . . 94

4.3.3 Technical Specications of the TéléTweez . . . 96

4.4 Mechatronics Design . . . 97

4.4.1 Actuator System Design . . . 97

4.4.2 Mechatronic Design of the TéléTweez. . . 107

4.5 Dynamics Analysis and Virtual Environment Application . . . 110

4.5.1 Dynamic Modeling . . . 110

4.5.2 Frequency Bandwidth Identication . . . 113

4.5.3 Virtual Environment Application . . . 114

4.6 Conclusion. . . 116

Conclusions and Future Works 119

A Geometric Optimization of Mechanical Amplier 123

B Static Analysis of Ball Screw 127

C Publication List 129

List of Figures

1.1 Microworld Environment . . . 6

1.2 Scale eect . . . 7

1.3 AmScope optical microscope . . . 9

1.4 Scanning electron microscope . . . 10

1.5 Indirect force sensor: force measurement from vision system . . . 11

1.6 Indirect force sensor: force transfered from working site to base . . . 11

1.7 Indirect force sensor: force measurement based on the model of actuator 12 1.8 Direct force sensor: thermal microgripper . . . 12

1.9 Direct force sensor: capacitative force sensor . . . 13

1.10 Micro-manipulation systems in research eld. . . 14

1.11 High accuracy machines for large batch microsystem automation . . 15

1.12 Chronogrip system by Percipio Robotics . . . 16

1.13 Chronogrip components . . . 16 1.14 PiezoGripper . . . 17 1.15 Piezoelectric eect . . . 19 1.16 Stack actuator . . . 19 1.17 Bimorph actuator . . . 20 1.18 Stepping actuators . . . 21

1.19 Microgripper based on electrostatic principle. . . 21

1.20 Microgripper based on SMA . . . 22

1.21 MRF by LORD Inc. . . 23

1.22 Virtuose haptic interface . . . 25

1.23 PHANToM haptic interface . . . 26

1.24 1 DOF Dual-Stage Interface . . . 26

1.25 Haptic interface Omega 7 by Force Dimension . . . 27

1.26 Haptic interface Pantograph by McGill university . . . 28

1.27 Cable interface and magnetic suspension interface . . . 28

2.1 Commercial microrobotic platform using piezoelectric stick-slip actu-ators. . . 35

2.2 The operation principle of the stick-slip actuator . . . 37

2.3 Forward and backward motions of stick-slip slider . . . 38

2.4 CAD view of the microrobotic system . . . 41

2.5 Simplied scheme of the piezoelectric stick-slip actuator . . . 41

2.6 Bloc diagram of the Prandtl-Ishlinskii static hysteresis model . . . . 43

2.7 Elastic and plastic components of relative motion . . . 44

2.8 Elasto-plastic phases evolution in stick-slip sequence . . . 46

2.9 Experimental setup for model identication . . . 49

2.10 Step response of the PE (stick-slip actuator without slider) using a 90 V step excitation . . . 50

viii List of Figures

2.11 Step response of the stick-slip actuator using a 40 V step excitation . 51

2.12 Experimental and simulation results of the identied PI model . . . 51

2.13 Characteristic of the break-away elastic strain versus input saw-tooth amplitude . . . 53

2.14 Comparison in the time domain between experimental and simulation data for dierent input sawtooth frequency condition in 20V . . . 54

2.15 Comparison in the time domain between experimental and simulation data for dierent input sawtooth frequency condition in 40V . . . 55

2.16 Comparison in the time domain between experimental and simulation data for dierent input sawtooth frequency condition in 60V . . . 56

2.17 Comparison in the frequency domain between experimental and simu-lation data between dierent input sawtooth conditions: 20V, 500Hz and 40V, 50Hz . . . 57

2.18 Velocity control scheme with PID approach . . . 58

2.19 Velocity control simulation with partial dynamic model. . . 59

3.1 Cantilever beam . . . 63

3.2 Dual-stage mechanical architecture . . . 65

3.3 Optical tweezers scheme . . . 66

3.4 Dual-stage haptic interface components: the Pantograph and Haptuator 69 3.5 Application of signal crossover in audio domain . . . 70

3.6 The bloc diagram illustrates the connection between crossover and dual-stage devices. . . 70

3.7 The system scheme about haptic information ow . . . 71

3.8 Magnitude plot of the LR-4 crossover . . . 72

3.9 System dynamic modeling . . . 73

3.10 PSD analysis (Welch) for the low frequency channel. . . 76

3.11 PSD analysis (Welch) of the high frequency channel . . . 77

3.12 System bloc diagram with compensation and crossover . . . 78

3.13 Magnitude response of the haptic interface . . . 80

3.14 Optical Tweezers manipulation scenario . . . 81

3.15 Histogram of measured acceleration on haptic handle while a Brow-nian motion is displayed from a microprobe . . . 82

3.16 Optical Tweezers application: non-contact and contact scenarios. . . 83

4.1 The da Vinci Surgical System . . . 87

4.2 Servomedics electronic tweezers . . . 87

4.3 The haptic user interfaces for training in virtual environments . . . . 89

4.4 The haptic tweezers of the project NeuroArm for robotic surgery . . 89

4.5 The haptic tweezers of the project NeuroArm for robotic surgery . . 90

4.6 Tweezers designed and manufactured by Dumont company . . . 91

4.7 The tweezers 707 from Ideal-tek . . . 92

4.8 The rst typical gesture to use tweezers in watchmaking process. . . 93

List of Figures ix

4.10 The third typical gesture to use tweezers in watchmaking process . . 94

4.11 Robotic control mode . . . 95

4.12 The schematic diagram of the actuator system. . . 98

4.13 The actuator system concept using ERF . . . 100

4.14 The actuator system concept using MRF . . . 101

4.15 The actuator system concept using stack piezoelectric material . . . 102

4.16 The pressure subsystem of the TéléTweez concept . . . 104

4.17 The concept of the TéléTweez based on a DC motor and ball screw. 105 4.18 Ball screw of Rockford . . . 105

4.19 Ball screw transmission eciency . . . 106

4.20 Scheme of transmission . . . 108

4.21 Backlash-free link by magnetic attraction . . . 108

4.22 TéléTweez CAD and prototype . . . 109

4.23 Dynamic modeling of the TéléTweez . . . 111

4.24 Accelerator setup to measure the bandwidth of the TéléTweez . . . . 114

4.25 Frequency bandwidth of the TéléTweez . . . 114

4.26 Controller setup for application . . . 115

4.27 Control scheme for virtual environment application . . . 115

4.28 Virtual environment application . . . 116

A.1 Geometry analysis of the mechanical amplier . . . 123

A.2 The schematic diagram of the optimized mechanical amplier . . . . 125

B.1 Analysis of ball screw mechanics. . . 127

List of Tables

1.1 A list of forces as a function of distance . . . 8

1.2 Comparison of various materials for micro-actuators . . . 24

1.3 Comparison of various haptic interfaces . . . 32

2.1 Comparison among typical piezoelectric stepping actuators. . . 37

2.2 Comparison among several friction models . . . 39

2.3 Model variables in elastic phase . . . 47

2.4 Model variables in mixed phase . . . 47

2.5 Model variables in plastic phase . . . 47

2.6 Model variables in initial motion reversal . . . 47

2.7 Model variables in initial motion reversal . . . 48

2.8 Identied parameters of the dynamic modeling . . . 52

3.1 Lowest natural frequencies of a beam for various materials . . . 64

3.2 Comparison of desktop haptic devices performances . . . 67

3.3 Parameters of dynamic modeling. . . 74

3.4 1/3 Octave-Band. . . 79

4.1 Comparison of dierent types of smart materials . . . 88

4.2 The characteristics of the Ideal-tek 707 tweezers . . . 92

4.3 Technical Specications of the TéléTweez . . . 97

4.4 Comparison of dierent types of smart materials . . . 99

4.5 Comparison of dierent types of PI piezoelectric products . . . 103

4.6 Commercial ball screw products . . . 106

4.7 Evaluation of the Actuator system options . . . 107

4.8 Comparison between desired technical Specications and the perfor-mance of the TéléTweez prototype . . . 110

General Introduction

As a recent research domain, micro-robotics deals with the study and application where a robot interacts with microscopic objects. The environment where such an interaction takes place is often mentioned as microworld and it contains ob-jects whose dimension covers from 1 µm to 1 mm [Régnier 2008]. With the rapid progress of science and technology, the industrial integration level becomes much more advanced and the miniature products more popular in our lives [Sun 2002] [Wang 2007] [Sitti 1998] [Romano 2012]. The micro-mechanics, the microsystems, the optics, the micro-electronics, and the biologies are all fast developing industries where ecient and reliable micro-manipulation (especially microassembly) makes a critical dierence.

Nowadays, dedicated systems for massive production of microsystems such as MEMS are already available in the market. The extensively adopted method to increase productivity is parallel microassembly: deposit a great amount of micro-components in a predened matrix pattern on a dedicated pad and then ip it over to align the pad to the other one, which carries the matched micro-components arranged in the same pattern. One example of such technique is ip-chip bonding. Such method is ecient, but restricted to a specic type of product. The blossom of microsystems industry implies a great variety of systems designs and many of them involve small series of complex products. In the case of small batches, adopting product specic parallel microassembly method gives rise to frequent redesign of carrying tools and iteration of all related processes such calibration and alignment. As a result, a more exible production method must be developed to answer the market window of small series micro-components manufacturing.

Cobotics, a neologism from the combination of the words "cooperation" and "robotics" [Peshkin 2001] [Gillespie 2001] [Chanphat 2006], provides a promising solution to tackle small series of complex production. It refers to a system that establishes collaboration between people and robots. The objective of cobotics is to automate a large range of tasks but keep in close collaboration with operators. Contrary to automation, cobotics emphasizes that people are the source of innova-tion and should remain central [Vinci-Energies 2014]. Cobotics can be considered as a method to promote exibility but maintain a high quality of productivity.

Under the collaboration between the MICROB group of the Institute for Intel-ligent Systems and Robotics (ISIR) of Pierre-and-Marie-Curie University and Per-cipio Robotics, the objective of this thesis is to design and realize the rst desktop cobotic platform dedicated to micro-manipulation. However, it is not to construct a new cobotic system but to build upon the existing cobotic platform Chronogrip, designed and realized by Percipio Robotics. It is focused on the key issues that arise in cobotics during the interaction between people and robots as well as the execution of motion command by slave system. A qualied cobotic system must enable desired information ows in mutual directions between operators and robots:

2 General Introduction

without sophisticated knowledge about how robots work behind, operators can in-tuitively deliver operation commands via the interface of the cobotic system, and the slave system must be able to realize desired trajectory and convey necessary information via the interface back to operators. That means, in the aspect of slave system, the dynamics of the actuator system must be studied and a sophisticated motion control strategy must be implemented to realize desired trajectory; in the aspect of user interface, the mechatronic design of interface must be intuitive to operators for the dedicated application and a set of algorithms must be designed and implemented to guarantee the quality of information ows. Concretely, three specic research objectives are dened below:

Research objective 1: Nonlinear dynamic modeling for a class of microrobotic systems using piezoelectric stick-slip actuators. For a teleoperation task of cobotic platform, velocity control is crucial for uent operation. This issue concerns the study of positioning actuator. Piezoelectric stick-slip actuator that used in Chrono-grip system is promising solution to realize a great range of microrobotic applica-tions, and many innovation companies have commercialized this kind of product with reasonable price. However, none of these companies or any research results is able to propose a complete control strategy for velocity. The main diculty lies in the complexity of the dynamics of piezoelectric stick-slip actuators. More pre-cisely, no research result has been reported to be able to fully describe the dynamics of such actuator. The rst research objective is to develop the dynamic model of the piezoelectric stick-slip actuator, in order to prepare for sophisticated trajectory tracking strategies for the cobotic platform.

Research objective 2: Developing a method to extend the bandwidth of dual stage haptic interface to render high dynamic haptic information from micro-environment. The cobotic platform to realize is dedicated to microrobotic applications. In the microworld, surface forces are more dominant due to scale eect. In such situa-tion, thermal agitation and other environmental elements cause the micro-objects to follow high dynamic motions. As a consequence, this will lead to high dynamic interaction forces between target objects and gripper tools. Taking into account the mechanical structure and design of the existing haptic interface, no option has enough bandwidth to render high dynamics arisen from microrobotic applications. The lack of high bandwidth haptic interface causes the interaction with the mi-croworld non-intuitive and inecient. In this case, the second objective is to develop a method to extend the bandwidth of haptic interface. The haptic interface used in the thesis is based on dual stage design. With this method, the cobotic platform will be able to render high-bandwidth haptic information.

Research objective 3: Design of an intuitive haptic interface for watchmaking process. One of the target application elds of our cobotic system is the prestigious watchmaking industry. In this sector, due to its exibility of models and small batch

General Introduction 3

production, the manufacturing process can hardly be automated. But handmade process has saturated accuracy and productivity, which makes the watchmaking players more and more dicult to conquer their place in global competition. One most important issue to apply Chronogrip to watchmaking process lies in the design of interface. Actually the general purposed interface installed in Chronogrip is way too dierent from the conventional tools used by watchmaking experts, and hence they have to be trained very hard to be familiar with the interface. Furthermore, there is no haptic feedback which makes the process nonintuitive. Nowadays, there is not yet a haptic interface based on a tweezers form available in prototype. The combination of realizing haptics and maintaining mechanical properties of tweezers is a challenging task. The third objective of the thesis is to address issue: design an intuitive haptic interface for watchmaking process.

The thesis is organized as follows: Chapter 2 is focused on the dynamic model-ing and development of a novel velocity control strategy for a class of nano-robotic systems using stick-slip linear actuators. The dynamic modeling of stick-slip linear actuators is able to describe the dynamics in both frequency and time domain. With the knowledge of the dynamic model, a sophisticated nonlinear control strategy will be developed for complete trajectory tracking; Chapter 3 is dedicated to the devel-opment of a novel method which applies signal crossover to extend the frequency bandwidth up to 1 kHz. Within the bandwidth, the haptic display can be rendered uniformly. The method is implemented in a dual-stage haptic interface and nally a haptic optical tweezers application is demonstrated; Chapter 4 is dedicated to the design of an intuitive haptic interface for watchmaker industry. The concept is pro-totyped, and analyzed in dynamics; The nal section concludes the thesis, followed by the bibliography.

Chapter 1

State-of-the-Art

Contents 1.1 Microrobotics . . . 6 1.1.1 Microworld . . . 6 1.1.2 Observation . . . 8 1.1.3 Micro-Manipulation Systems . . . 13 1.1.4 Chronogrip System . . . 15

1.1.5 Flexible Micro-Manipulation Solutions . . . 17

1.2 Actuators for Microrobotic Applications . . . 17

1.2.1 Piezoelectric Actuators. . . 18

1.2.2 Electrostatic Actuators . . . 20

1.2.3 Thermal Actuators . . . 21

1.2.4 Magneto-/Electrorheological Fluids. . . 22

1.2.5 Actuators for Microrobotic Applications . . . 22

1.2.6 Control Algorithm for Piezoelectric Stick-Slip Actuator . . . 23

1.3 Haptic Interface . . . 24

1.3.1 Series-Structure Interface . . . 25

1.3.2 Parallel-Structure Interface . . . 27

1.3.3 Haptic Interfaces Summary . . . 29

1.3.4 Dedicated Haptic Interfaces for Micro-Manipulation . . . 29

1.4 Challenges. . . 29 This chapter will rstly introduce the basic physics of the microworld and the existing observation methods. Then it describes the available technologies of micro-manipulation systems as well as what is still missing. To address the need, some challenges must be handled in terms of actuator and haptic interface for micro-manipulation. The current development of those two aspects will be introduced in the second and third sections. Finally, specic research objectives of the thesis will be summed up in the last section.

µ 1 mm 100 m 10 m 1 m 100 nm 10 nm 1 nm Microworld Macroworld Nanoworld µ 3 2 _F vol Fsur Fvol Fsur

Fvol Fsur

•

•

8 Chapter 1. State-of-the-Art

involved, the volume of the liquid, the property of the material, the distance between two solids and their geometry.

As can be seen from the description above, those forces are highly related to the separation distance. According to the study [Lee 1991], a classication of forces is listed in the table 1.1as a function of separation distance.

Interaction range Force type

Innity gravity

A few nm to 1 mm capillary force > 0.3 nm electrostatic force > 0.3 nm van der Waals force < 0.3 nm molecular interactions 0.1 - 0.2 nm chemical interactions

Table 1.1: A list of forces as a function of distance [Lee 1991].

1.1.2 Observation

The microworld is far beyond human perceptive capabilities. Dedicated tools must be developed to allow observation in this special environment. For research and engineering purpose, position measurement and force sensing are two of the most important perception tasks. They remain, however, dicult to carry out.

1.1.2.1 Position measurement

In recent years, various technologies have been developed to observe microworld. They are based on dierent physical mechanisms and could lead to dierent op-eration principles: one could interact directly with the target object and provide image frame in run time; the other may not ask direct interaction but reconstruct the desired image in an asynchronous manner. The type of equipment to choose depends on the specic application, where requirement of precision, position range, time response vary largely from one to the other.

To date, the most common methods of position measurement in the microworld are visual based. In particular, two methods are widely applied: optical micro-scope and scanning electron micromicro-scope (SEM). Those two methods are both able to visualize micro objects of size between 1 µm and 1 mm.

• Optical microscope also referred to as light microscope, is a system built with lenses and mirrors. It provides the user with magnied image of small samples. Typical optical microscope can be very simple to set up, though complex components can be added to improve image resolution or contrast. Figure1.3 is an example of AmScope optical microscope [AmScope 2015]. In terms of performance, there are several limitations:

1.1. Microrobotics 9

- eld of view, which decreases when resolution is increased;

- depth of eld, which degrades the same manner as eld of view, and can only cover a very thin layer due to the focus plane.

Figure 1.3: AmScope optical microscope B120C-E1 [AmScope 2015].

• Scanning electron microscope often abbreviated as SEM, provides an alterna-tive option for position measurement in the microworld. Instead of relying on photons as the working principle of optical microscope, SEM is based on elec-trons. Briey, streams of electrons, emitted by an electron emitter gun, are reected when they come into contact with target objects. During interaction, emissions of back-scattered electrons, X-rays, etc. are resulted. Captured by some specic sensors, an image of the target object's surface can be recon-structed. Figure 1.4 illustrates an example of SEM system designed by FEI [FEI 2015] and a typical image produced by SEM for material science. Compared to optical microscope, SEM has innite depth of eld. However, it has a larger response time in the order of 500 ms. Some other limitations must also be taken into account. One major consideration is that the electron beam can also interact with any medium along the space between the tar-get object and the electron emitter gun. The medium includes air molecules. As a consequence, SEM requires the sample be placed in a vacuum cham-ber. Furthermore, the sample must be conductive so that no electric charge accumulated on them.

1.1.2.2 Force measurement

To x ideas, the amplitude of generated force in micro-scale is typically in the order of micro-Newton to milli-Newton. This directly gives rise to the requirement that the force sensor must be extremely sensitive and be compatible with the microworld environment, if based on contact approach. Furthermore, the absence of reliable measurement techniques and the lack of multi-axis sensors with required resolution lead to impediment to the measurement force applied to micro objects. In addition to the requirement of force sensor described above, the force measurement system must also be able to comply with several conditions [Régnier 2008]:

10 Chapter 1. State-of-the-Art

(a) (b)

Figure 1.4: (a) FEI Verios XHR SEM; (b) An image example for material science [FEI 2015].

- it must ensure adequate grip. Particularly too much grip can lead to severe deformation or damage to target objects or even sensor components;

- it may require sophisticated strategy to control insertion strength during assem-bly process. Position plus force control is a classical challenge in macro environment, which becomes more dicult in the microworld context;

- it can faithfully detect if a contact is made when critical vision information is not available.

The current available force measurement approaches can be classied as indirect and direct methods.

• Indirect measurement methods: due the space limitation, a range of indirect approaches have been developed in the literature. Several popular methods are described below:

- Force measurement by vision system: this kind of method usually requires no physical contact and can deliver force measurement from remote computa-tion. To implement such method, a camera or laser sensor must be equipped, as well as fast and faithful image processing algorithms (e.g. pattern recogni-tion). Research work can be found in the studies [Greminger 2004] [Anis 2006] [Wang 2001]. The working principle relies on the prerequisite knowledge of me-chanical property of the tool. Typically, based on the exion or deformation of the tool detected by image processing, the interaction force can be computed with the knowledge of the tool's mechanical properties [Chang 2009]. This method liberates additional force sensing equipment on the working site, but gives rise to complex vision electronic system. Furthermore, the corresponding algorithm must be able to produce fast and faith processing result, which is still a challenging issue today. The gure1.5 illustrates the vision method.

16 Chapter 1. State-of-the-Art

Figure 1.12: Chronogrip system by Percipio Robotics.

play, this kind of user interface will be referred to as a haptic interface. For Chronogrip system, a touch screen is provided as an alternative teleoperation interface.

• The coupling system refers to the set of electronic and software components which can enable the bidirectional communication. Concretely, it can convey the motion command (desired position, velocity, or acceleration, etc.) from master device to slave device and send back the information of manipulation (haptic feedback, etc.) from slave device to master device in run time. • The high resolution vision system zooms viewpoint in the micro-world

envi-ronment which goes beyond the capability of the human naked eyes.

• The robotic positioning system provides multiple degrees of freedom in both translation and orientation with high resolution and large range. The actuator implemented in Chronogrip is piezoelectric stick-slip actuator.

(a) (b) (c)

Figure 1.13: Chronogrip components: (a) tablet unidirectional interface; (b) vision device; (c) positioning system.

• Percipio Robotics has developed their own gripping device called PiezoGripper (see the gure1.14). It is based on piezoelectric benders, each actuated on two directions (horizontal and vertical). With two benders, it is possible to build

1.2. Actuators for Microrobotic Applications 17

a two ngered gripper, with 4 independent degrees of freedom. Horizontal motion of both ngers is used to the grasping/release of micro-objects, the vertical motion is used to align the ngertips of the gripper.

(a) (b)

Figure 1.14: (a) PiezoGripper mounted on a miniature robotic arm; (b) Fully inte-grated PiezoGripper.

1.1.5 Flexible Micro-Manipulation Solutions

There is currently a market window between large batch automation and small batch handmade process. Flexible micro-manipulation solutions are urgently demanded by small and medium-sized enterprises that want to launch innovative, hybrid and highly miniaturized components as small- to medium-scale production.

As a starting point, the cobotic platform Chronogrip is a promising solution for exible micro-manipulation, but not yet complete. One missing part is the con-trol algorithm to realize accurate trajectory tracking. Solutions provided today is limited. This topic is challenging and concerns deep study of actuators for the mi-crorobotic system. Another issue concerns human-robot interaction. It is believed that in order to realize intuitive and eective interaction, haptic feedback is in-dispensable. Haptic functionalities are still absent in Chronogrip platform. More fundamental problem lies in the fact that existing haptic interfaces are general pur-posed with moderate performance, but they are not able to address the challenges from micro-manipulation. Much more eorts are needed for new design and meth-ods.

In order to understand the challenges, the next two sections will rstly survey available actuators and haptic interfaces for microrobotic applications.

1.2 Actuators for Microrobotic Applications

An actuator is one of the central components of a robotic system. It converts other types of energy, such as electrical, magnetic or thermal energies, to mechanical en-ergy, so as to provide desired force and displacement specied by a control unit. In microrobotics, the demand for the development of reliable and precise actuators of

18 Chapter 1. State-of-the-Art

size compatible with microrobotic applications is urgent and challenging. Potential applications include wide elds such as automotive (airbag, microsensors), biomed-ical, aeronautical and spatial industries. However, technologies of actuator applied in conventional industries such as hydraulic, pneumatic and electric motor-based are commonly not suitable to be transferred for micro and millimeter scales. Their prop-erties such as resolution, eciency cannot address challenges in microrobotics when they are miniaturized. Therefore, it is unavoidable to call on dierent materials and innovative working principles to address the needs in microrobotics.

Nowadays, more and more energies are dedicated to development of actuators for microrobotics. Some popular options are:

• piezoelectric actuators, • electromagnetic actuators, • electrostatic actuators, • thermal actuators, • shape memory alloys, • magnetostrictive actuators, • electro-active polymers,

• electrorheological uids (ERF) and magnetorheological uids (MRF).

The criteria for choosing appropriate actuators may depend on the specications of applications, such as resolution, motion stroke, blocking force, power/weight ratio, cost of fabrication, and dynamics for control aspect (frequency bandwidth, linearity, technical feasibility).

In the following text, some of the most widely used options are surveyed. 1.2.1 Piezoelectric Actuators

Piezoelectric actuators can realize bidirectional conversion between electric energy and mechanical energy. The family of piezoelectric actuators has various working principle but all based on the piezoelectric eect. The physical phenomenon was rstly demonstrated by Pierre and Jacques Curie in 1880, in naturally occurring crystals. The direct eect consists of polarization of the material under the eects of mechanical stress. On the contrary, the inverse eect refers to a mechanical deformation on application of an electric eld. Therefore, piezoelectric materials can be characterized by electromechanical coupling. Piezoelectric eect is illustrated by the gure 1.15.

Based on dierent congurations and aimed for various applications, there are several kinds of actuators as derivatives of piezoelectric materials that are described below:

• Stack (multilayer) actuators. This type of actuators consists of multiple layers of piezoelectric materials separated by insulating layers. Power supply of same

•

24 Chapter 1. State-of-the-Art Piezoelectric Thermal bimorph SMA

Physical process piezoelectricity:_{dipole orientation} dierence in ther-mal expansion co-ecients

solid phase transi-tion

Operation

princi-ple electric eld thermal thermal

Energy density (J.m−3₎

106 _{(PZT), 10}3

(PMN) 105 Ni/Si 106 to 107

Bandwidth high (100 kHz) low, geometry de-_pendent low, geometry de-_{pendent, (10}2_{) Hz}

Mode of operation depends on orien-tation of electric eld

exion exion,tension, compres-torsion, sion

Deformation 0.12-0.15% 5.23 × 10−4_/◦_{C 1-15%} Conductive

poly-mer Gianttostrictionmagne- MRF/ERF Physical process

oxidation and re-duction eect ion diusion

magnetostriction: orientation of magnetic dipole

particle chains formed along ux lines

Operation

princi-ple voltage magnetic eld magnetic/electriceld Energy density

(J.m−3₎ 103

104 _{to 10}5 (Ter-fenol D)

Bandwidth low (10 Hz) high (100 kHz) high Mode of operation exion, tension,_compression depends on orien-tation of magnetic

eld viscosity

Deformation 1-5% 0.58-0.81% 

Table 1.2: Comparison of various materials for micro-actuators [Bellouard 2002].

1.3 Haptic Interface

In the process of human-microworld interaction, operation intuitiveness and eec-tiveness can be achieved by providing haptic display. Actually, versatile micro-manipulation platforms that have been demonstrated recently often use techniques from haptic feedback teleoperation for micro-manipulation [Bolopion 2013]. The purpose of haptics is to give an illusion that the operator directly worked with the target object without any medium in between. In other words, the haptic interface can serve as an extension of human body for inaccessible working environment. In recent years, tremendous studies are dedicated to the development of haptic inter-faces. The available technologies can be mainly characterized by some properties

1.3. Haptic Interface 25

such as: the degree of freedom (DOF) in motion and in haptic space, the geometry of working space, the maximum rendering forces back to user, the frequency band-width of haptic information, and etc. In terms of modeling issue, haptic interface can be eciently described as an inertia with a damping component [Diolaiti 2006]. In this section, some popular haptic interfaces that employed in micro-manipulation are surveyed in the following.

1.3.1 Series-Structure Interface

Inspired by commercialized industrial robots, a range of haptic interfaces based on series structure can be found, especially in commercial market. Briey, such kind of haptic interface benets from large working space, easier integration of orientation. Particular issue arises from the actuator distribution along the mechanical structure in chain. This signicantly increases the overall inertia, reduce the resultant stiness. The dynamics must be considered before using in any haptic application. In the following text, some popular haptic interfaces based on series structure are surveyed.

1.3.1.1 Virtuose

The haptic interface Virtuose is commercialized in 1999 by Haption [Haption 2015], which is the subsidiary of French public government-funded research organization CEA (Commissariat à l'énergie atomique et aux énergies alternatives). The Virtuose 6D35-45 provides haptic feedback in 6 DOF with maximum rendering force as 35 N. The geometry of the working space is a sphere with 450 mm as diameter. The version Virtuose 3D15-25 has 3D haptic rendering with the maximum force as 15 N and the diameter of the working space is 250 mm. The models are shown in the gure1.22.

(a) (b)

× × 3

1.3. Haptic Interface 27 1.3.2 Parallel-Structure Interface

Though having its working space signicantly reduced compared to series structure, the advantage of haptic interface based on parallel structure lies in the fact that the actuators and sensors can be implemented near the base. This design greatly reduces the inertia in mechanical chain and enhances the overall stiness. As a result, the dynamic performance, e.g. the frequency bandwidth, is greatly promoted compared to its series rivals.

1.3.2.1 Omega 7

Originally developed by Virtual Reality and Active Interface group in EPFL (École Polytechnique Fédérale de Lausanne), the haptic interface Omega is a popular in many research and industrial domains. In 2001, the design is commercialized by Force Dimension (Lausanne Switzerland) [ForceDimension 2016]. The interface is based on parallel structure DELTA and has 3 DOF as translation. The latest version Omega 7 (see the gure 1.25) has 3 DOF for haptic feedback, a working space of 160 ×110 mm as translation and 240 × 140 × 180 deg as rotation. The maximum force it can provide is 12 N.

Figure 1.25: Haptic interface Omega 7 by Force Dimension [ForceDimension 2016].

1.3.2.2 Pantograph

The haptic interface Pantograph (see the gure1.26) is rstly developed in 1994 by the haptics laboratory in McGill university, Canada [Campion 2005b]. It is based on a planar parallel mechanism, actuated by 2 motors at base. The linkage is optimized to be sti and light. The working space is about 10 × 16 cm2 _{and the maximum} output force is 10 N.

1.3.2.3 Cable Interface

Ideal haptic interface based on cable transmission can maximum explored working space with minimum obstacle from mechanical chain. One well known example is

1.4. Challenges 29

is oat due to magnetic eld. The position and orientation are measured precisely by optical sensors. This type of interface has very high dynamic performance. 1.3.3 Haptic Interfaces Summary

This section has survey some of the most popular haptic interfaces used in micro-manipulation. They are based on general-purposed design so as to be applied in a wide range of applications. However, being general leads to a compromise among performance properties such as the degree of freedom (DOF) in motion and in haptic space, the range and geometry of working space, the maximum rendering forces back to user, the dynamic range (ration between maximum temporary force and friction; with 1 mN as minimum value as threshold of perception), and etc. A more complete survey is summarized in the table 1.3.

1.3.4 Dedicated Haptic Interfaces for Micro-Manipulation

Nowadays, the available haptic interfaces are still far from being qualied with respect to the need required by micro-manipulation, which may demand a combi-nation of the performance properties described above. For example, some advanced microrobotic applications require large working space and large frequency band-width. Typical existing solutions employ cantilever structure to augment working space, however, the frequency bandwidth must be reduced due to the dynamics of cantilever design. Another example is some special micro-manipulation may re-quire dedicated interface design to enhance operation intuitiveness, where general purposed haptic interfaces can hardly fulll the request.

In summary, available haptic interface solutions cannot fully address the needs from micro-manipulation. Eorts are still needed in haptic interface mechanical design and the development of related algorithms to realize intuitive and eective micro-manipulation.

1.4 Challenges

This chapter has introduced the basics of microrobotics, and the existing technolo-gies for micro-manipulation. As discussed, there is a blank window for small batch production of complex microsystems, which demands exible solution to address the need. Under such circumstances, Percipio Robotics has proposed its semi-automatic cobotic platform Chronogrip to bridge the cap between prevailing non-exible mass automation and low-yield handmade process. However, the solution is not yet com-plete, there is still challenges in terms of trajectory tracking and haptic rendering. Concretely, there are three problems to resolve:

• In the human-robot interaction, control in velocity is crucial. This issue con-cerns the study of positioning actuator. Piezoelectric stick-slip actuator that used in Chronogrip system is promising solution to realize a great range of mi-crorobotic applications, and many innovation companies have commercialized

30 Chapter 1. State-of-the-Art

this kind of product with reasonable price. However, none of these companies or any research results is able to propose a complete control strategy for veloc-ity, let alone acceleration control. The main diculty lies in the complexity of the dynamics of piezoelectric stick-slip actuators. More precisely, no research result has been reported to be able to fully describe the dynamics of such actuator. To be more general, no control strategy is available nowadays to address complete trajectory tracking for piezoelectric stick-slip actuator, and its dynamics is not yet fully understood.

• In the microworld, surface forces are more dominant due to scale eect (see the section 1.1.1.1). In such situation, thermal agitation and other environ-mental elements cause the micro-objects to follow high dynamic motions. As a consequence, this will lead to high dynamic interaction forces between tar-get objects and gripper tools. Taking into account the existing mechanical structure and design of the haptic interface, no option is able to render high dynamics arisen from microrobotic applications. The lack of high bandwidth haptic interface causes the interaction with the microworld non-intuitive and inecient.

• In prestigious watchmaking industry, due to its exibility of models and small batch production, the manufacturing process can hardly be automated. But handmade process has saturated accuracy and productivity, which makes the watchmaking players more and more dicult to conquer their place in global competition. To address this challenge, Percipio Robotics proposes Chrono-grip to realize cobotic production. However, the most signicant issue lies in the interface. A joystick or tablet is way too dierent from the conventional tools (the tweezers) used by watchmaking experts, and hence they have to be trained very hard to be familiar with the interface. Furthermore, there is no haptic feedback which makes the process nonintuitive. Nowadays, there is not yet a haptic interface based on a tweezers form available in prototype. The combination of realizing haptics and maintaining mechanical properties of tweezers is a challenging task.

The objective of the thesis is not to construct a new cobotic platform for micro-robotics, but aimed to address the three challenges described above.

The rst challenge concerns the issue of the development of trajectory tracking strategies for piezoelectric stick-slip actuator. Particularly, velocity control is the subset of this general tracking challenge. In order to handle this issue, a thorough study of the actuator dynamics must be conducted. Today, modeling methods have been proposed by various studies, but none of them is able to describe the dynamics completely, meaning the lack of description in time and frequency domain, for stepping and scanning mode and for backward and forward motion. In chapter 2, the study of nonlinear dynamic modeling for a class of microrobotic systems using piezoelectric stick-slip actuators is conducted. It will show that the model can

1.4. Challenges 31

describe the dynamics for all the three aspects mentioned above. This result paves the way for the next development of trajectory tracking strategies.

The second challenge concerns the study of bandwidth of haptic interface. Large bandwidth is important for the realization of high dynamic interaction for micro-manipulation. In chapter 3, analytical results show that cantilever interface (what-ever the material) cannot lead to satisfying bandwidth for micro-manipulation. To handle this issue, a method is proposed to extend the bandwidth of dual stage hap-tic interface by using signal crossover technique. With the method implemented, experimental results show that the dual stage interface has an extended bandwidth from DC to 1 kHz.

The third challenge concerns design of a novel haptic interface for watchmak-ing process. The particularity is that the interface must resemble a conventional tweezers to promote intuitiveness. In chapter 4, it will show that diculties arise when providing haptics and tweezers-based characteristics must be satised simulta-neously. Realization of actuator system is the most challenging part, where several candidate solutions are proposed and evaluated. A nal design will be presented as well as the rst prototype. Since it is tweezers-based design and is compatible with conventional usage, the interface is not limited to watchmaking and can be used in a wide range of micro-manipulations.

32 Chapter 1. State-of-the-Art

Supplier Product _DOF

H-DOF W ork space (cm) Peak force (N) Con tin ue fo rce (N) Friction (N) Dynamic range Percep. in erti al (g) Stiness (N/mm) Structure Novint Falcon 3 3 8 9 >₃₀₀ 8 P Force dimen-sion Omega 3 3 3 11 12 12 0.3-0.5 40 14.5 P Force dimen-sion Delta 3 3 3 32 20 14.5 P Force dimen-sion Delta 6 6 6 32 20 14.5 P

3D Systems Phantom_Omni 6 3 11 3.3 0.88 0.3-_0.5 3 45 1-_2.3 S 3D Systems Phantom_Desktop 6 3 23 7.9 1.5-_2.3 S

3D Systems Phantom_1.5 6 3 27 8.5 1.4 75 3.5 S

3D Systems Phantom 3 6 3 58 22 1 S

Quanser 5-DOF_Wand 6 5 38 7-9 2-3 6 H

Quanser HD2 _{6 5 41}

14-20 8-11 0.35 40-57 300 3 P

Haption Virtuose 3D_Desktop 6 3 20 10 3 2 S

Haption Virtuose 6D_Desktop 6 6 20 10 3 2 S

Haption Virtuose 6D 6 6 84 31 8.5 2 S Haption Inca 6D 6 6 150 37.5 12.5 C MPB Tech-nologies Freedom 6S 6 6 22 2.5 0.6 0.06 42 100-200 S Buttery Haptics Maglev 200 6 6 2.4 40 0 4×104 510 50 P ACROE Laboratory ERGOSMRK n n 2 200 60 0.005 4×104 300 40 P Moog HapticMaster 3 3 36 250 100 2000 50 S [Campion 2005b] Pantograph 2 2 10 10 10 55 P [Mohand-Ousaid 2012] dual-stage 1 1 5 5 0.003 6 S

Table 1.3: Comparison of various haptic interfaces. P, S, H and C represent parallel, series, hybrid and cable. H-DOF is DOF for haptics. Phantom Omni and Phantom Desktop are now named as Geomatic Touch and Geomatic Touch X respectively.

Chapter 2

Nonlinear modeling for a class of

microrobotic systems using

piezoelectric stick-slip actuators

Contents

2.1 Introduction . . . 35

2.2 State-of-the-Art . . . 36

2.2.1 Microrobotic Actuators . . . 36

2.2.2 Working Principle of Piezoelectric Stick-Slip Actuator . . . . 37

2.2.3 Friction Modeling . . . 38

2.3 Presentation of the microrobotic system . . . 40

2.4 Nonlinear dynamic modeling . . . 40

2.4.1 Dynamic Modeling of the PE and the slider . . . 41

2.4.2 Modeling of the Slider . . . 42

2.4.3 Modeling of the Friction . . . 43

2.5 Experimental analysis and identication . . . 48

2.5.1 Description of the experimental setup . . . 48

2.5.2 Parameters identication . . . 49

2.5.3 Model Validation . . . 53

2.6 Discussion . . . 55

2.7 Velocity Control . . . 57

2.8 Conclusions . . . 59 In order to develop trajectory tracking strategies for microrobotic systems, the dynamics of an elementary actuator must be studied and well modeled. This chapter addresses modeling issues for a class of microrobotic systems using piezoelectric stick-slip actuators. The modeling of this kind of actuators is complex because: (i) several parameters of the system (i.e. dynamics of the piezoelectric material itself, the friction dynamics and the dynamics of the moving slider) are nonlinear and coupled, (ii) there is no systematic methodology for parameters identication and (iii) existing friction models are often limited due to the complexity of the presliding motion. The consequence is that existing models are quite accurate for a small working range (i.e. input voltage and input frequency ranges). This is not

34 Chapter 2. Nonlinear modeling for a class of microrobotic systemsusing piezoelectric stick-slip actuators sucient when the microrobotic systems are involved for both large displacements (e.g. millimeter range) and small displacements (i.e. micrometer range). The main contribution of this chapter is the proposition of an extended dynamic model for microrobotic systems using piezoelectric stick-slip actuators. The main issues that have been addressed are:

• modeling of hysteresis. This is not as simple as for traditional piezoelectric actuators because here both the hysteresis of the piezoelectric element and the friction dynamic are involved.

• improving the single-state elasto-plastic friction model. In this study, we show that several low frequency vibration modes of the stick-slip piezoelectric actu-ator are not due to the piezoelectric element itself, but it is due to the friction contact. A multi-state elasto-plastic friction model is then used. Moreover, we show for the rst time how the break-away displacement can evolve with the amplitude and the frequency of an input sawtooth signal. Results show that this dependence is not the same when the actuator is moving in a forward direction and in a backward direction.

• obtaining a complete coupled nonlinear model being able to describe the dy-namics of stick-slip type actuators for both scanning mode and stepping mode in the time and the frequency domains and for backward and forward direc-tions of the motion.

Results of this chapter open new perspectives for cinematic and dynamic models of robotic systems intended to do tasks at the micro scales. Therefore results can be used for the development of dedicated velocity and/or position control.

The model is validated with experimental data. At last, a velocity control strat-egy is demonstrated.

• • •

36 Chapter 2. Nonlinear modeling for a class of microrobotic systemsusing piezoelectric stick-slip actuators chapter, a velocity control application is demonstrated. The study is based on the theory of the single state elasto-plastic model and on a series of experiments.

In the next section, some popular microrobotic actuators and modeling ap-proaches are surveyed. In the section 2.3, the global architecture of the studied microrobotic system and its main features are presented. The section 2.4deals with the nonlinear modeling of the system taking into account the friction contact force and the hysteresis nonlinearity. In the section 2.5, the experimental analysis and the model identication are presented. A discussion on the modeling issues is given in the section 2.6. In parallel with the development of complete dynamic model (e.g. inverse modeling), a non-model based velocity control scheme is demonstrated in the section 2.7.

2.2 State-of-the-Art

2.2.1 Microrobotic Actuators

In microrobotics, piezoelectric-based actuators are getting increased market shares because of their desirable properties such as compact size, high resolution, fast response and high power to weight ratio. Increasing the actuation range can be achieved through amplication (bender) or stepping motion [Breguet 2007]. Various solutions using stepping motion are widely used in many applications such as micro-biology, neurology, micro-material assembly. So far, piezoelectric-based actuators which are based on stepping motion principle can be mainly classied into three categories [Li 2013] [Breguet 2007]: ultrasonic actuators, inchworm actuators, and inertial actuators. They bear some common characteristics such as their motion are friction based, the travel range depends only on slider's length, and they have a holding force without any power consumption. However, they dier in working principle and performance.

Typical ultrasonic actuator relies on the excitation of resonance of the sta-tor. This vibration is generally elliptical and is used to drive the load by friction [Vasiljev 2007] [Kanda 2006] [Morita 2000]. Motion direction can be controlled by shifting phase sign among dierent piezo components. Such actuators are featured by high speed (> 100 mm/s). In terms of control, they provide a medium control-lability and are sensitive to variations of loads. The control unit can be complex to implement due to the need to track resonance [Cedrat 2015].

Inchworm actuator has its slider (load) always in contact with alternate preloaded piezo stators. The guided motion mainly depends on the driving fre-quency and the phase shift among stator groups. The accurate synchronization among piezo stators is the key to guarantee desired motion [Lu 2009] [Moon 2006] [Kim 2002]. Such actuators can provide much higher forces and resolution, but are relatively slow (< 10mm/s) with respect to other two options. The corresponding control unit could also be expensive to realize multi-phases based working principle. Inertial actuator's working principle is based on the competition between the inertial force and friction force. It can be operated in either scanning or stepping

2.2. State-of-the-Art 37 mode depending on the choice between high resolution motion and large range mo-tion [Belly 2012] [Yang 2011] [’piller 2011] [Fung 2008]. Generally, such actuator provides medium speeds (10-50 mm/s). Instead of multi-phases based design as de-scribed from the previous two options, a typical inertial actuator is composed of only one piezoelectric channel. This simplicity lowers the cost, promotes response speed, leads to a better miniaturization potential, and greatly reduces the complexity in control aspect.

Piezoelectric stick-slip actuator is one of the most widely used inertial actuators. Based on the simplicity described above, it is believed that piezoelectric stick-slip actuator is a promising choice for microrobotics and it is chosen to build up our micro-manipulation cobotic system. The comparison among those three actuators is summarized in the table 2.1.

Ultrasonic Inchworm Inertial

Resolution sub-micron sub-nm sub-nm

Velocity > 100 mm/s < 10 mm/s 10-50 mm/s Piezoelectric channel multiple multiple single Travel range < slider's length < slider's length < slider's length

Force < 40 N < 800 N < 10 N

self-locking self-locking self-locking Table 2.1: Comparison among typical piezoelectric stepping actuators.

2.2.2 Working Principle of Piezoelectric Stick-Slip Actuator

Piezo Position : Stick

Time (a) (b) Stick Slip 1 step Slider Piezo Slider Piezo

Piezo Position : Slip

Time Piezo Slider Slider Piezo Ff Ff Friction material

Figure 2.2: The operation principle of the stick-slip actuator. (a) Stick phase; (b) Slip phase.

38 Chapter 2. Nonlinear modeling for a class of microrobotic systemsusing piezoelectric stick-slip actuators A piezoelectric stick-slip actuator is made of (gure 2.2) a Piezoelectric Element (PE), a slider moving along a linear axis and a friction material between the PE and the slider. The slider is in charge of carrying a load (e.g. robot axis). It is guided by the deformable PE that converts electrical energy to mechanical energy. During a slow deformation of the PE, the contact friction force Ff drives the slider to a linear motion (gure 2.2(a)). After an abrupt contraction of the PE, the slider slips and cannot fully follow the sudden motion of the PE because the inertia force becomes greater than the contact friction force. The slip phase is illustrated in gure 2.2(b). An alternate stick and slip sequence produces a displacement of the slider relative to the PE. By repeating those operations, large range of motion of the slider can be achieved. This function mode is called stepping mode. The input voltage signal applied to the PE is a sawtooth sequence so that alternate slow and abrupt deformations can be realized. If there is only stick motion without any slip, the slider can be driven with higher precision. This function mode is called scanning mode. Unlike conventional motors, motion direction cannot be changed by inverting input power. If input sawtooth sequence is given by repeating slow rise and abrupt drop, the actuator goes towards one direction, which will be referred to as forward direction; the opposite direction can be produced if sawtooth sequence is given by repeating abrupt rise and slow drop, and this direction will be referred to as backward direction, as shown in the gure 2.3.

(a)

(b)

Slider Piezo

Forward direction Voltage

Time

Slider Piezo

Backward direction Voltage

Time

Figure 2.3: Simplied scheme showing that the direction of motion of the slider can be specied by the drive direction of the input sawtooth voltage.

2.2.3 Friction Modeling

Due to the dynamic complexity of the piezoelectric stick-slip actuators, many research and industrial applications employ static models [Breguet 1998] [Bergander 2003] [Rakotondrabe 2009] [Rakotondrabe M 2009]. Such typical so-lution describes the actuator velocity as a linear function of the input sawtooth frequency and amplitude. It is a simple and ecient approximation. However, such models can only be used for stepping mode within a limited input condition range, and is not suitable for scanning mode. In the research work [Peng 2011], a dynamic model is developed. But the model is only validated in time domain for several input

2.2. State-of-the-Art 39 condition and for only one motion direction. The validation in frequency domain is absent.

As described previously, The phenomenon of stick-slip is determined by the con-tact friction force in dynamic conditions. As a nonlinear phenomenon, friction is considered as one of the most dicult challenges in mechatronic systems and it can cause control problems such as static errors and limit cycles [Lampaert 2003]. Therefore, friction modeling is considered as the crucial part of the dynamic mod-eling of piezoelectric stick-slip actuator.

Friction model Continuity Presliding Non-drifting Stribeck Nb. of

(stiction) states Regularized Coulomb √  Karnopp √  Dahl √ √ single LuGre √ √ √ single Single-state elasto-plastic √ √ √ √ single GMS √ √ √ √ multiple

Table 2.2: Comparison among several friction models.

In the literature, various friction force models can be found, but they are not all suitable for microrobotic applications. The Karnopp friction model is a combination between Coulomb and viscous force [Karnopp 1985]. It is a simple approximation and widely used. Nevertheless, the sign function in the model can cause discontinu-ity in numerical implementation. The regularized Coulomb model [Threlfall 1978] made a compromise between friction properties and numerical continuity. Further-more, if high precision positioning and low velocity tracking are required, those two models can not give rise to satisfactory results [De Wit 1995]. In order to address the high precision positioning and tracking in microrobotics, a comprehensive fric-tion model must be employed to describe the phenomenon of presliding which is the motion prior the complete slip [Dupont 2002]. The Leuven model [Lampaert 2002] [Swevers 2000] and GMS model [Lampaert 2003] are multi-state complex models established in asperity level. The latter one is the most comprehensive and is able to describe complex behaviors such as presliding regime, Stribeck eect, frictional lag, transition behavior and etc. However, in order to obtain smooth and accurate fric-tion signals, there must be sucient number of states (asperities). This complexity could be a major impediment for real-time applications where computational time must be strictly controlled. The LuGre model [De Wit 1995] [De Wit 1993], in line with the Dahl model [Dahl 1968], is a single-state friction model which is based on the average behavior of the bristles. This model can describe presliding, Stribeck eect and frictional lag [Zhong 2011]. However, its limitation is that it exhibits undesirable drift behavior [Hayward 2000].

40 Chapter 2. Nonlinear modeling for a class of microrobotic systemsusing piezoelectric stick-slip actuators To tackle this issue, Dupont et al. [Dupont 2002] have proposed a single-state elasto-plastic friction model that reduces the drift while it preserves the fa-vorable properties of existing models. This model has been applied in several stud-ies [Seran 2003] [Buechner 2012] [Han 2011]. In particular, the research work [Peng 2011] [Rakotondrabe 2009] use this friction model to develop dynamic model for piezoelectric stick-slip actuator. However, none of those research work has rig-orously investigated how to incorporate this friction model for dierent motion di-rections. This seems trivial, but in our study, it will be demonstrated that special condition must be met in order to address motion direction change. Indeed, in the original paper [Dupont 2002] it is suggested that some parameters of the model would be changed in case of direction change. For control purposes, the model must be able to simulate the dynamic motion of the actuator in a wide operating range and for both forward and backward motions.

Based on the simplicity and versatility of the single-state elasto-plastic model, it is chosen as the friction model in our study. As mentioned above, additional condition of the friction model must be specied so as to address dierent motion directions. The comparison of friction models is summarized in the table 2.2.

2.3 Presentation of the microrobotic system

The microrobotic system is designed by SmarAct company. It is composed of a 6 DOF parallel robot and a 3 DOF Cartesian robot (see the gure 2.4). Each axis of the microrobot is actuated by a piezoelectric stick-slip actuator of the same reference (SLC-1720-S-HV). The maximum stroke of each axis in the Cartesian microrobot is 12 mm, the maximum amplitude of the input driving voltage is 100 V and the scanning resolution is in submicron range. The study is mainly concerned with the dynamic modeling of the stick-slip actuator. The actuator of the Y axis in the Cartesian structure is used for the experimental validation. The motion of this actuator is measured with a laser interferometer sensor (SP-120 SIOS Mebtechnik GmbH).

2.4 Nonlinear dynamic modeling

To dene the dynamic model of the complete microrobotic system, the dynamics of each axis must be well modeled. As such, the challenge is to dene an accurate dynamic model of an elementary stick-slip actuator.

The major impediment lies in the fact that the internal structure is no public information. As such, hypothesis must be made for the modeling. There are three main assumptions (Fig. 2.5):

(i) the Piezoelectric Element (PE) is attached to the base of the actuator, (ii) the moving slider is guided by a linear crossed roller guideway and has only one translational DOF,

! " # !$%#&' "$%#&' #$%#&' x1 x2 x y Piezo Element Slider Linear guide Ff Ff Base Mp d2x1a dt2 + Dpa dx1a dt + Kpax1a= Kact1aU − Ff Mp d2x1b dt2 + Dpb dx1b dt + Kpbx1b= Kact1bU − Ff x1 = x1a+ x1b Mp Dpi Kpi Kact1i